If light were an electromagnetic wave

...would the world be a very different place? Quantum theory originally had to deal with huge problems in classical physics, above all the stability of atoms. The particle theory of light evolved in the context of experiments like the photo-electric effect and the Compton effect. In pre-Schroedinger days, these phenomena did indeed seem like compelling evidence for the particle theory. Later developments showed, however, that they could also be explained with classical light. Write the Hamiltonian and put in a sinusoidally varying electric field, and pretty much everything works as it ought to: the photo-electric effect, the Compton effect, etc.

Nowadays the strongest evidence for photons comes from recent experiments on anticorrelation statistics of single-photon detection. My question is then: to what end? Suppose the anti-correlation experiments had been done and the opposite result were obtained...consistent with classical e-m. Would that result have been such a disaster? Would it have implied any irreconcilable contradictions with the universe as we know it?

The particle theory of light is not the only thing that led to QM. Consider for example the problem with black body radiation and incorrect atom models. I think even without the particle theory we would eventually have come to the same conclusion (but in a different order). Now, light was found to have wave/particle duality first, and all other particles followed later. Maybe without light particles we would have found that all particles should have the wave/particle duality, and as a result so would light.

First of all , Photo electric effect cannot be explained using classical theroy(Maxwell Electromagnetism,according to the classical theory the energy of the emitted electron should be proportional to the intensity of light, but that is Not the case), your another point using Sinusoida equations in perturbation : the way of solving the equation is an approximate, we should replace the field with Field operators,for exact prediction we need to use quantum field theory(it is a successfull theroy but not a complete theory).

The photoelectric effect has nothing to do with photons, this myth is only perpetuated to avoid embarassing Einstein (who won his Nobel prize for his wrong explanation of the photoelectric effect). The photoelectric effect can be correctly described in terms of classical light waves interacting with a quantum mechanical atom, this is discussed in many papers and books, an accessible one is "The Quantum Challenge" by Greenstein and Zajonc, chapter 2 "Do photon's exist?"

The modern understanding is that photons exist, but only in extremely delicate quantum experiments. The first experimental proof of the existence of photons came in the early 1980s, for which Alain Aspect won his Nobel prize.

The light that comes out of a lightbulb is not made out of photons. Technically, it is not in a photon number eigenstate and so if you exressed the light wave as being made of photons you would see that it is in an infinite superposition of photon states. Each of the photon states would individually look like a particle (this is what Aspect managed to detect) but when they are all superposed together the individual particles disappear and an electromagnetic wave emerges. This is why most of the posts on this forum which contain the word "photon" are totally nonsense, since for some reason students find photons vastly more interesting than classical E&M waves, even though both exist in seperate situations.

Greenstein and Zajonc do not (and are not attempting to) disprove Einstein's explanation for the phototelectric effect, they merely offer a plausible alternative explanation. The fact of the matter, however, is we do not which one (if either) is correct and for you to claim otherwise is nonsense.

Greenstein and Zajonc do not (and are not attempting to) disprove Einstein's explanation for the phototelectric effect, they merely offer a plausible alternative explanation.

I never claimed otherwise, I just said "can be correctly described."

The fact of the matter, however, is we do not which one (if either) is correct and for you to claim otherwise is nonsense.

Just because we have an alternative explanation of the photoelectric effect, we may not know which is correct, yes. But this isn't the basis for my claim, which is:

Technically, it [the light from a light bulb] is not in a photon number eigenstate and so if you exressed the light wave as being made of photons you would see that it is in an infinite superposition of photon states. Each of the photon states would individually look like a particle (this is what Aspect managed to detect) but when they are all superposed together the individual particles disappear and an electromagnetic wave emerges.

Civilized is very right to point out that something is very wrong with the explanation of the photo-electric effect. The common explanation consists of two pieces: first, the photon business, which can perhaps be ultimately justified; and second, the business of debunking the wave theory of light. It's the second half which is clearly wrong, as Civilized shows with references.

I am not completely sure that Einstein is personally guilty of the second half. I haven't read his original paper, but I know he was a very deep thinker and had his own reasons (possibly incorrect) which drew him to the particle theory. What is baffling is how a very wrong explanation has gained so much popular currency. I actually doubt this has been done to spare Einstein's feelings. It is more plausible to me that it is to spare the feelings of the Nobel Committee who awarded Einstein the prize for what was probably the weakest of his many contributions.

Einstein Was Right at that time or right to predict few experiment results(it is like Newtons Gravational theory which should replaced by General theory of Relativity), it is the way scientists develop science( the only possible way)

The fact that the typical state of light is some superposition of photon number eigenstates, still does not mean that light is an electromagnetic wave.

The electromagnetic wave only appears in the classical limit where you have macroscopic electromagnetic fields, you can then ignore commutators between photon creation and annihilation operators. Only in this limit do you get the Maxwell equations.

The general evolution of electromagnetic fields is described by a Schrödinger wave functional. Given an initial electromagnetic field configuration, you can compute the amplitude that it will evolve to some final field configuration in some time. The formal solution of this can be written as a path integral.

In the classical limit hbar ---> 0 the dominant contribution to the path integral becomes that evolution which minimizes the action and you regain Maxwell's equations. Letting hbar go to zero is formally equivalent to keeping hbar equal to 1 and considering the evolution of fields in the limit they become infinitely strong.

The fact that the typical state of light is some superposition of photon number eigenstates, still does not mean that light is an electromagnetic wave.

Are you sure that this is not just a matter of semantics? For me it is wrong to say X is made of a bunch of Ys, when there is no experiment or observation that can ever be done in principle to show that that particular specimen of X is made of Ys. In other words, there is no way to observe that the light from a light bulb is made of photons, this conclusion only comes about by applying reductionist reasoning. I am condensed matter physicist, so I favor the semantics of emergence over reductionism. What I see is that in the light from a lightbulb there is no way (experimentally) to reduce the phenomenon to photons, therefore classic lightwaves are an emergent phenomenon that arise from superpositions of photon number eigenstates. Therefore, in these case where lightwaves cannot be experimentally reduced to photons, I would say that the lightwave is just as real as the photons that are observed in e.g. Aspect's experiment.

The electromagnetic wave only appears in the classical limit where you have macroscopic electromagnetic fields, you can then ignore commutators between photon creation and annihilation operators. Only in this limit do you get the Maxwell equations.

I agree, but do you think that liquids exist? Do you think that water is a liquid? Afterall, liquids are just made of molecules. How would you react to a thread with the title "What if water was a liquid?" where the implict line of discussion is that water is not actually a liquid because the navier-stokes equations only arise in the limit of macroscopic averaging.

I prefer to regard liquid water as we know as just as real as H2O molecules. Liquid water is a phenomenon that emerges from H2O molecules, just as light waves are a phenomenon that emerge from photons.

The general evolution of electromagnetic fields is described by a Schrödinger wave functional. Given an initial electromagnetic field configuration, you can compute the amplitude that it will evolve to some final field configuration in some time. The formal solution of this can be written as a path integral.

In the classical limit hbar ---> 0 the dominant contribution to the path integral becomes that evolution which minimizes the action and you regain Maxwell's equations. Letting hbar go to zero is formally equivalent to keeping hbar equal to 1 and considering the evolution of fields in the limit they become infinitely strong.

I agree with all of this, but just because something is a mathematical limit in some model does not make it any less real. Reality has to do with what it is possible to observe in principle. It is not possible to observe a lightwave as a mere collection of photons, because it is actually a quantum superposition of various numbers of photons. If you like, when I say "light really is an E&M wave" you can replace with "light really is a wooby-do, where a wooby-do is distinctly different from just a collection of photons and a wooby-do has all the properties of an electromagnetic wave."

Can you explain Super fluidity of a liquid based on classical methods?

Whether or not this is possible is irrelevant to the discussion at hand. My point is that water is a liquid and in the same sense light is an electromagnetic wave. In both cases the entities are composite, but in each case they have emergent properties which cannot be reduced to the constituent parts. The quantum case of superfluids is even better suited to making my point than a classical fluid, because it is more similar to light in this sense: in both light and superfluids the emergent behaviors arise from quantum effects like superposition and state entanglement which are even more difficult to reduce to photons/fermions.

,Black Body Spectrum is an example for the existence of photons

Hmm, I am familiar with the derivation of the black body spectrum based on the bose statistics of a photon gas, but this is just a model. There are dozens of models based on photons that give very accurate predictions, for example QED, the most precisely tested theory of all. But hopefully everyone understands that just because photons predict the right answer does not mean they really exist (or else we would be relatively close to proving that fundamental strings exist ;), that what needs to be done is to detect actual photons, and this was first done by Alain Aspect in 1981 as several posters in this thread have recognized.

You can derive the specific heat of solids by replacing the lattice vibrations by "particles" called phonons. The black body spectrum is similar. Just because you can do it mathematically with a particle-based calculation doesn't mean there aren't real vibrations actually taking place.

In a solid it's the wave nature of atoms that is responsible for the higher-frequency modes "freezing out" at low temperatures. Without these high-frequency modes, there is nothing to couple to the high-frequency electromagnetic modes. That's the basis of one semi-classical derivation of the black-body spectrum.

In fact, you can call Planck's derivation semi-classical: except he kept the atoms classical and quantized the light instead of vice versa. Is it surprising that you can also derive the same result by quantizing the matter and keeping the light classical?

As Civilized points out, there are many ways of deriving the black body spectrum. I haven't found it yet but I'm pretty sure you can derive it by examining the equilibrium of a single electron in a box (the well-known "potential well") with a classical electromagnetic field.

But you quantize the energy in each mode and the quantum is called the photon in case of electromagnetism, a phonon in case of lattice vibrations.
You can play the same game in case of Fermions. To obtain electrons you must quantize the Dirac field interpreted as a classical anti-commuting field.

So, if we are sceptical about photons, then we should also call into question if electrons, quarks, and thus atoms really exist. Who knows, perhaps you can write down some fundamenal theory which you can approximately solve by introducing the Standard Model fields as "ghost fields". So, whenever we do an experiment involving a macroscopic aparatus, we can compute the probability of the outcome of a masurement by pretending as if electrons and photons exist and adding up the amplitudes according to certain rules.

So, if we are sceptical about photons, then we should also call into question if electrons, quarks, and thus atoms really exist.

I haven't seen anyone in this thread who is skeptical about photons. I have repeated that Alain Aspect won the Nobel Prize for work done in the 1980s that conclusively demonstrates the existence of photons.

I do see people in this thread who are skeptical about the fact that light is an electromagnetic wave , but I am arguing that this is a matter of semantics, asking "What if light were an electromagnetic wave?" is just like asking "What if water were a liquid?"

The photoelectric effect has nothing to do with photons, this myth is only perpetuated to avoid embarassing Einstein (who won his Nobel prize for his wrong explanation of the photoelectric effect). The photoelectric effect can be correctly described in terms of classical light waves interacting with a quantum mechanical atom, this is discussed in many papers and books, an accessible one is "The Quantum Challenge" by Greenstein and Zajonc, chapter 2 "Do photon's exist?"

The modern understanding is that photons exist, but only in extremely delicate quantum experiments. The first experimental proof of the existence of photons came in the early 1980s, for which Alain Aspect won his Nobel prize.

The light that comes out of a lightbulb is not made out of photons. Technically, it is not in a photon number eigenstate and so if you exressed the light wave as being made of photons you would see that it is in an infinite superposition of photon states. Each of the photon states would individually look like a particle (this is what Aspect managed to detect) but when they are all superposed together the individual particles disappear and an electromagnetic wave emerges. This is why most of the posts on this forum which contain the word "photon" are totally nonsense, since for some reason students find photons vastly more interesting than classical E&M waves, even though both exist in seperate situations.

I think I agree with what you are saying but I'm not sure. Are you saying that all thermal phenomena e.g the spectrum of a hot gas are the same whether you analyze it in terms of photons or if you take the semi-classical system of Maxwellian light interacting with quantum atoms? That's the conclusion I'm leaning towards.

The photoelectric effect has nothing to do with photons, this myth is only perpetuated to avoid embarassing Einstein (who won his Nobel prize for his wrong explanation of the photoelectric effect). The photoelectric effect can be correctly described in terms of classical light waves interacting with a quantum mechanical atom, this is discussed in many papers and books, an accessible one is "The Quantum Challenge" by Greenstein and Zajonc, chapter 2 "Do photon's exist?"